scholarly journals К теории формирования крупных трещин в хрупких твердых телах

2021 ◽  
Vol 63 (7) ◽  
pp. 923
Author(s):  
Ю.А. Хон ◽  
П.В. Макаров
Keyword(s):  
Crack Initiation ◽  
Uniform Distribution ◽  
Phase Field ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Field Method ◽  
Phase Field Method ◽  
Spatial And Temporal Scales ◽  
Brittle Solids ◽  
Nonlinear Parabolic

A model of the large cracks formation in brittle solids is formulated taking into account different space-time scales of crack accumulation during deformation. Within the framework of the phase field method, a system of two coupled nonlinear parabolic equations is obtained that describe the deformation of a loaded medium during crack initiation on two spatial and temporal scales. The conditions are found under which the uniform distribution of cracks becomes unstable. The development of instability is accompanied by the formation of large cracks.

Crack kinking and tunneling simulation for the single-fiber composite under transverse tension based on phase-field method

2020 ◽  
Vol 55 (5-6) ◽  
pp. 145-158
Author(s):  
Leying Song ◽  
Songhe Meng ◽  
Chenghai Xu ◽  
Guodong Fang ◽  
Qiang Yang ◽  
...  
Keyword(s):  
Numerical Model ◽  
Crack Initiation ◽  
Phase Field ◽  
Three Dimensional ◽  
Field Method ◽  
Fiber Reinforced Composites ◽  
Phase Field Method ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Transverse Tension

Virtual tests for a single-fiber–reinforced composite model subjecting to transverse tension are carried out based on a phase-field method considering a varying interface toughness parameter. Without pre-treating the crack initiation location and propagation path, the complete fracture process is realized for the first time in a three-dimensional numerical model, including nucleation cracks on the fiber/matrix interface at the free end, tunneling cracks along the fiber axis, and kinked interface cracks deviating from the interface and penetrating into the matrix. The numerically calculated crack propagation process is in good agreement with the in situ observations in the literature, indicating that the present model provides a good real-time quantitative numerical method for three-dimensional fracture analysis of fiber-reinforced composites. Tunneling cracks tend to cause macroscopic interface debonding and fiber pull-out. The interface tunneling crack initiation and the transition to the steady state inside the model are captured and analyzed in the numerical model. Kinked interface cracks can merge with other matrix cracks, forming a macroscopic transverse crack fracture mode. The kinking behaviors affected by the initial crack size and the interface properties are investigated. This study for the detailed crack propagation is helpful in understanding the toughening mechanism of fiber-reinforced composites under transverse tension.

scholarly journals On the choice of parameters in the phase field method for simulating crack initiation with experimental validation

2016 ◽  
Vol 197 (2) ◽  
pp. 213-226 ◽  
Author(s):  
T. T. Nguyen ◽  
J. Yvonnet ◽  
M. Bornert ◽  
C. Chateau ◽  
K. Sab ◽  
...  
Keyword(s):  
Crack Initiation ◽  
Phase Field ◽  
Experimental Validation ◽  
Field Method ◽  
Phase Field Method

Kinetics of oxidation of ammonia on cobalt catalyst I model of the reactor with catalytically active wall

1982 ◽  
Vol 47 (8) ◽  
pp. 2087-2096 ◽  
Author(s):  
Bohumil Bernauer ◽  
Antonín Šimeček ◽  
Jan Vosolsobě
Keyword(s):  
Parabolic Equations ◽  
Cobalt Catalyst ◽  
Nonlinear Parabolic Equations ◽  
Catalytic Reactions ◽  
Temperature Profiles ◽  
Dimensional Model ◽  
Kinetics Of Oxidation ◽  
Nonlinear Parabolic ◽  
Catalytically Active ◽  
Kinetics Of

A two dimensional model of a tabular reactor with the catalytically active wall has been proposed in which several exothermic catalytic reactions take place. The derived dimensionless equations enable evaluation of concentration and temperature profiles on the surface of the active component. The resulting nonlinear parabolic equations have been solved by the method of orthogonal collocations.

scholarly journals Harnack’s inequality for doubly nonlinear equations of slow diffusion type

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
Verena Bögelein ◽  
Andreas Heran ◽  
Leah Schätzler ◽  
Thomas Singer
Keyword(s):  
Vector Field ◽  
Harnack Inequality ◽  
Parabolic Equations ◽  
Full Range ◽  
Nonlinear Parabolic Equations ◽  
Growth Conditions ◽  
Diffusion Type ◽  
Slow Diffusion ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear

AbstractIn this article we prove a Harnack inequality for non-negative weak solutions to doubly nonlinear parabolic equations of the form $$\begin{aligned} \partial _t u - {{\,\mathrm{div}\,}}{\mathbf {A}}(x,t,u,Du^m) = {{\,\mathrm{div}\,}}F, \end{aligned}$$ ∂ t u - div A ( x , t , u , D u m ) = div F , where the vector field $${\mathbf {A}}$$ A fulfills p-ellipticity and growth conditions. We treat the slow diffusion case in its full range, i.e. all exponents $$m > 0$$ m > 0 and $$p>1$$ p > 1 with $$m(p-1) > 1$$ m ( p - 1 ) > 1 are included in our considerations.

Theoretical phase-field-method-based model of the γ phase dissolution of base metals in duplex stainless steels

2021 ◽  
Vol 26 ◽  
pp. 102150
Author(s):  
Dong-Cho Kim ◽  
Tomo Ogura ◽  
Ryosuke Hamada ◽  
Shotaro Yamashita ◽  
Kazuyoshi Saida
Keyword(s):  
Phase Field ◽  
Stainless Steels ◽  
Field Method ◽  
Duplex Stainless Steels ◽  
Phase Field Method ◽  
Base Metals ◽  
Phase Dissolution
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